查看更多>>摘要：In the last forty years,the rise of HIV has undoubtedly become a major concern in the field of public health,imposing significant economic burdens on affected regions.Consequently,it becomes imperative to undertake comprehensive investigations into the mechanisms governing the dissemination ofHIV within the human body.In this work,we have devised a mathematical model that elucidates the intricate interplay between CD4+T-cells and viruses of HIV,employing the principles of fractional calculus.The production rate of CD4+T-cells,like other immune cellsdepends on certain factors such as age,health status,and the presence of infections or diseases.Therefore,we incorporate a variable source term in the dynamics of HIV infection with a saturated incidence rate to enhance the precision of our findings.We introduce the fundamental concepts of fractional operators as a means of scrutinizing the proposed HIV model.To facilitate a deeper understanding of our system,we present an iterative scheme that elucidates the trajectories of the solution pathways of the system.We show the time series analysis of our model through numerical findings to conceptualize and understand the key factors of the system.In addition to this,we present the phase portrait and the oscillatory behavior of the system with the variation of different input parameters.This information can be utilized to predict the long-term behavior of the system,including whether it will converge to a steady state or exhibit periodic or chaotic oscillations.
查看更多>>摘要：Recently,planar collections of Feynman diagrams were proposed by Borges and one of the authors as the natural generalization of Feynman diagrams for the computation of k=3 biadjoint amplitudes.Planar collections are one-dimensional arrays of metric trees satisfying an induced planarity and compatibility condition.In this work,we introduce planar matrices of Feynman diagrams as the objects that compute k=4 biadjoint amplitudes.These are symmetric matrices of metric trees satisfying compatibility conditions.We introduce two notions of combinatorial bootstrap techniques for finding collections from Feynman diagrams and matrices from collections.As applications of the first,we find all 693,13 612 and 346 710 collections for(k,n)=(3,7),(3,8)and(3,9),respectively.As applications of the second kind,we find all 90 608 and 30 659 424 planar matrices that compute(k,n)=(4,8)and(4,9)biadjoint amplitudes,respectively.As an example of the evaluation of matrices of Feynman diagrams,we present the complete form of the(4,8)and(4,9)biadjoint amplitudes.We also start a study of higher-dimensional arrays of Feynman diagrams,including the combinatorial version of the duality between(k,n)and(n-k,n)objects.
查看更多>>摘要：Based on the long wave limit method,the general form of the second-order and third-order rogue wave solutions to the focusing nonlinear Schrödinger equation are given by introducing some arbitrary parameters.The interaction solutions between the first-order rogue wave and one-breather wave are constructed by taking a long wave limit on the two-breather solutions.By applying the same method to the three-breather solutions,two types of interaction solutions are obtained,namely the first-order rogue wave and two breather waves,the second-order rogue wave and one-breather wave,respectively.The influence of the parameters related to the phase on the interaction phenomena is graphically demonstrated.Collisions occur among the rogue waves and breather waves.After the collisions,the shape of them remains unchanged.The abundant interaction phenomena in this paper will contribute to a better understanding of the propagation and control of nonlinear waves.
查看更多>>摘要：Nonlinear circuits can show multistability when a magnetic flux-dependent memristor(MFDM)or a charge-sensitive memristor(CSM)is incorporated into a one branch circuit,which helps estimate magnetic or electric field effects.In this paper,two different kinds of memristors are incorporated into two branch circuits composed of a capacitor and a nonlinear resistor,thus a memristive circuit with double memristive channels is designed.The circuit equations are presented,and the dynamics in this oscillator with two memristive terms are discussed.Then,the memristive oscillator is converted into a memristive map by applying linear transformation on the sampled time series for the memristive oscillator.The Hamilton energy function for the memristive oscillator is obtained by using the Helmholtz theorem,and it can be mapped from the field energy of the memristive circuit.An energy function for the dual memristive map is suggested by imposing suitable weights on the discrete energy function.The dynamical behaviors of the new memristive map are investigated,and an adaptive law is proposed to regulate the firing mode in the memristive map.This work will provide a theoretical basis and experimental guidance for oscillator-to-map transformation and discrete map energy calculation.
查看更多>>摘要：The nonlinear Schrödinger(NLS)equation,which incorporates higher-order dispersive terms,is widely employed in the theoretical analysis of various physical phenomena.In this study,we explore the non-commutative extension of the higher-order NLS equation.We treat real or complex-valued functions,such as g1=g1(x,t)and g2=g2(x,t)as non-commutative,and employ the Lax pair associated with the evolution equation,as in the commutation case.We derive the quasi-Gramian solution of the system by employing a binary Darboux transformation.The soliton solutions are presented explicitly within the framework of quasideterminants.To visually understand the dynamics and solutions in the given example,we also provide simulations illustrating the associated profiles.Moreover,the solution can be used to study the stability of plane waves and to understand the generation of periodic patterns within the context of modulational instability.
查看更多>>摘要：A new type of symmetry,ren-symmetry,describing anyon physics and corresponding topological physics,is proposed.Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as super-symmetric quantum mechanics,super-symmetric gravity,super-symmetric string theory,super-symmetric integrable systems and so on.Super-symmetry and Grassmann numbers are,in some sense,dual conceptions,and it turns out that these conceptions coincide for the ren situation,that is,a similar conception of ren-number(R-number)is devised for ren-symmetry.In particular,some basic results of the R-number and ren-symmetry are exposed which allow one to derive,in principle,some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems.Training examples of ren-integrable KdV-type systems and ren-symmetric KdV equations are explicitly given.
查看更多>>摘要：In this paper,two types of fractional nonlinear equations in Caputo sense,time-fractional Newell-Whitehead equation(FNWE)and time-fractional generalized Hirota-Satsuma coupled KdV system(HS-cKdVS),are investigated by means of the q-homotopy analysis method(q-HAM).The approximate solutions of the proposed equations are constructed in the form of a convergent series and are compared with the corresponding exact solutions.Due to the presence of the auxiliary parameter h in this method,just a few terms of the series solution are required in order to obtain better approximation.For the sake of visualization,the numerical results obtained in this paper are graphically displayed with the help of Maple.
查看更多>>摘要：A protocol of quantum dense coding with gravitational cat states is proposed.We explore the effects of temperature and system parameters on dense coding capacity and provide an efficient strategy to preserve the quantum advantage of dense coding for these states.Our results may open new opportunities for secure communication and insights into the fundamental nature of gravity in the context of quantum information processing.
查看更多>>摘要：We establish tighter uncertainty relations for arbitrary finite observables via(α,β,γ)weighted Wigner-Yanase-Dyson((α,β,γ)WWYD)skew information.The results are also applicable to the(α,γ)weighted Wigner-Yanase-Dyson((α,γ)WWYD)skew information and the weighted Wigner-Yanase-Dyson(WWYD)skew information.We also present tighter lower bounds for quantum channels and unitary channels via(α,β,γ)modified weighted Wigner-Yanase-Dyson((α,β,γ)MWWYD)skew information.Detailed examples are provided to illustrate the tightness of our uncertainty relations.
Wentao QiAlexandr I ZenchukAsutosh KumarJunde Wu...
100-112页
查看更多>>摘要：Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations.Using the'sender-receiver'model,we propose quantum algorithms for matrix operations such as matrix-vector product,matrix-matrix product,the sum of two matrices,and the calculation of determinant and inverse matrix.We encode the matrix entries into the probability amplitudes of the pure initial states of senders.After applying proper unitary transformation to the complete quantum system,the desired result can be found in certain blocks of the receiver's density matrix.These quantum protocols can be used as subroutines in other quantum schemes.Furthermore,we present an alternative quantum algorithm for solving linear systems of equations.
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